Question

assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $3x\sqrt{72x^6y^3}$

Explanation:

Step1: Factor radicand into squares

$\sqrt{72x^6y^3} = \sqrt{36 \cdot 2 \cdot (x^3)^2 \cdot y^2 \cdot y}$

Step2: Simplify the radical

$\sqrt{36 \cdot 2 \cdot (x^3)^2 \cdot y^2 \cdot y} = 6x^3y\sqrt{2y}$

Step3: Multiply by outside term

$3x \cdot 6x^3y\sqrt{2y} = 18x^{1+3}y\sqrt{2y}$

Step4: Combine exponents of x

$18x^{4}y\sqrt{2y}$

Answer:

$18x^4y\sqrt{2y}$